Sample Clustering

K-means clustering

Chose k=3 as best number of clusters

set.seed(123)
wss = sapply(1:10, function(k) kmeans(datExpr_t, k, nstart=25)$tot.withinss)
plot(wss, type='b', main='K-Means Clustering')
best_k = 3
abline(v = best_k, col='blue')

datExpr_k_means = kmeans(datExpr_t, best_k, nstart=25)
clusterings[['KMeans']] = datExpr_k_means$cluster

Hierarchical Clustering

Chose k=7 as best number of clusters.

h_clusts = datExpr_t %>% dist %>% hclust %>% as.dendrogram
h_clusts %>% plot
abline(h=25, col='blue')

best_k = 7

Clusters seem to be able to separate ASD and control samples pretty well and there are no noticeable patterns regarding sex, age or brain region in any cluster.

Colors:

• Diagnosis: Blue=control, Green=ASD

• Sex: Pink=Female, Blue=Male

• Brain region: Pink=Frontal, Green=Temporal, Blue=Parietal, Purple=Occipital

• Age: Purple=youngest, Yellow=oldest

clusterings[['HC']] = cutree(h_clusts, best_k)

create_viridis_dict = function(){
  min_age = datMeta$Age %>% min
  max_age = datMeta$Age %>% max
  viridis_age_cols = viridis(max_age - min_age + 1)
  names(viridis_age_cols) = seq(min_age, max_age)
  
  return(viridis_age_cols)
}
viridis_age_cols = create_viridis_dict()

dend_meta = datMeta[match(labels(h_clusts), rownames(datMeta)),] %>% 
            mutate('Diagnosis' = ifelse(Diagnosis_=='CTL','#008080','#86b300'), # Blue control, Green ASD
                   'Sex' = ifelse(Sex=='F','#ff6666','#008ae6'),                # Pink Female, Blue Male
                   'Region' = case_when(Brain_lobe=='Frontal'~'#F8766D',        # ggplot defaults for 4 colours
                                        Brain_lobe=='Temporal'~'#7CAE00',
                                        Brain_lobe=='Parietal'~'#00BFC4',
                                        Brain_lobe=='Occipital'~'#C77CFF'),
                   'Age' = viridis_age_cols[as.character(Age)]) %>%            # Purple: young, Yellow: old
            dplyr::select(Age, Region, Sex, Diagnosis)
h_clusts %>% set('labels', rep('', nrow(datMeta))) %>% set('branches_k_color', k=best_k) %>% plot
colored_bars(colors=dend_meta)

Consensus Clustering

Chose the best clustering to be with k=8, which is basically two big clusters and some outliers

*The rest of the output plots can be found in the Data/Gandal/consensusClustering/samples_DE_genes folder

Independent Component Analysis

Following this paper’s guidelines:

0. Run PCA and keep enough components to explain 60% of the variance (The 2 first components explain over 60% of the variance, so decided to keep the first 37 to accumulate 90% of the variance)

1. Run ICA with that same number of nbComp as principal components kept to then filter them

2. Select components with kurtosis > 3

3. Assign obs to genes with FDR<0.01 using the fdrtool package

Note: Using the PCA reduced matrix because the algorithm didn’t converge with the original dataset

It’s not supposed to be a good method for clustering samples because ICA does not perform well with small samples (see Figure 4 of this paper)

Still, it leaves only 7 samples without a cluster

ICA_clusters %>% rowSums %>% table

## .
##  0  1  2  3  4  6 
##  7 36 23 10  3  1

# ICA_clusters %>% mutate(cl_sum=rowSums(.)) %>% as.matrix %>% melt %>% ggplot(aes(Var2,Var1)) + 
#   geom_tile(aes(fill=value)) + xlab('Clusters') + ylab('Samples') + 
#   theme_minimal() + theme(axis.text.x=element_blank(), axis.ticks.x=element_blank()) + coord_flip()

WGCNA

This method doesn’t work well:

Using power=5 as it is the first power that exceed the 0.85 threshold and the reduced version of the dataset because the original one never reaches the \(R^2\) threshold

best_power = datExpr_redDim %>% t %>% pickSoftThreshold(powerVector = 1:30)

##    Power SFT.R.sq  slope truncated.R.sq  mean.k. median.k.   max.k.
## 1      1   0.0873 -0.323         0.0532 1.60e+01  1.56e+01 2.64e+01
## 2      2   0.5580 -0.912         0.7120 4.65e+00  4.03e+00 1.11e+01
## 3      3   0.6670 -1.060         0.6750 1.64e+00  1.18e+00 5.18e+00
## 4      4   0.8300 -1.090         0.8940 6.53e-01  3.97e-01 2.58e+00
## 5      5   0.8970 -1.070         0.9420 2.85e-01  1.48e-01 1.34e+00
## 6      6   0.8970 -1.050         0.9570 1.33e-01  6.02e-02 7.17e-01
## 7      7   0.9240 -1.060         0.9560 6.53e-02  2.62e-02 3.91e-01
## 8      8   0.9440 -1.040         0.9700 3.35e-02  1.06e-02 2.16e-01
## 9      9   0.1710 -2.070        -0.0377 1.78e-02  4.29e-03 1.21e-01
## 10    10   0.1670 -2.010        -0.0484 9.77e-03  1.87e-03 6.86e-02
## 11    11   0.1610 -1.900        -0.0620 5.50e-03  8.30e-04 3.92e-02
## 12    12   0.1770 -2.610        -0.0381 3.16e-03  3.73e-04 2.25e-02
## 13    13   0.1410 -2.230        -0.1030 1.85e-03  1.70e-04 1.32e-02
## 14    14   0.7960 -0.898         0.8180 1.11e-03  7.80e-05 8.34e-03
## 15    15   0.1060 -1.460        -0.1200 6.69e-04  3.61e-05 5.33e-03
## 16    16   0.7870 -0.865         0.8090 4.10e-04  1.69e-05 3.44e-03
## 17    17   0.8150 -0.870         0.8420 2.55e-04  7.74e-06 2.24e-03
## 18    18   0.0489 -0.916        -0.0662 1.60e-04  3.45e-06 1.48e-03
## 19    19   0.0823 -1.600        -0.0938 1.01e-04  1.54e-06 9.78e-04
## 20    20   0.1180 -1.840        -0.1320 6.43e-05  6.86e-07 6.52e-04
## 21    21   0.1890 -1.680         0.0398 4.13e-05  3.07e-07 4.37e-04
## 22    22   0.1900 -1.700         0.0396 2.67e-05  1.38e-07 2.94e-04
## 23    23   0.1960 -2.360         0.0109 1.73e-05  6.20e-08 1.98e-04
## 24    24   0.1940 -2.300         0.0247 1.13e-05  2.79e-08 1.34e-04
## 25    25   0.2140 -2.680         0.0094 7.41e-06  1.26e-08 9.13e-05
## 26    26   0.2210 -2.640         0.0197 4.87e-06  5.70e-09 6.21e-05
## 27    27   0.1920 -2.590        -0.0360 3.22e-06  2.58e-09 4.23e-05
## 28    28   0.2100 -2.430         0.0107 2.13e-06  1.17e-09 2.89e-05
## 29    29   0.2230 -2.780         0.0014 1.42e-06  5.31e-10 1.98e-05
## 30    30   0.2300 -2.740         0.0104 9.42e-07  2.40e-10 1.35e-05

Running WGCNA with power=5

# Best power
network = datExpr_redDim %>% t %>% blockwiseModules(power=best_power$powerEstimate, numericLabels=TRUE)

##      mergeCloseModules: less than two proper modules.
##       ..color levels are 0, 1
##       ..there is nothing to merge.

Cluster distribution

table(network$colors)

## 
##  0  1 
## 41 39

clusterings[['WGCNA']] = network$colors
names(clusterings[['WGCNA']]) = rownames(datExpr_redDim)

Using the original expression dataset, the \(R^2\) threshold is never achieved, getting closest at power 1, but still doesn’t manage to find any clusters within the data

best_power = datExpr %>% pickSoftThreshold(powerVector = 1:30)

##    Power SFT.R.sq slope truncated.R.sq mean.k. median.k. max.k.
## 1      1    0.298 666.0         0.1110    77.9      77.9   78.2
## 2      2    0.297 333.0         0.1090    76.7      76.9   77.3
## 3      3    0.297 222.0         0.1090    75.6      75.8   76.5
## 4      4    0.296 167.0         0.1070    74.6      74.8   75.7
## 5      5    0.298 134.0         0.1080    73.5      73.8   74.9
## 6      6    0.297 112.0         0.1070    72.4      72.8   74.2
## 7      7    0.297  95.5         0.1060    71.4      71.9   73.4
## 8      8    0.296  83.5         0.1050    70.4      70.9   72.6
## 9      9    0.295  74.2         0.1030    69.4      70.0   71.9
## 10    10    0.298  67.3         0.1050    68.4      69.0   71.1
## 11    11    0.298  61.2         0.1040    67.4      68.1   70.4
## 12    12    0.297  56.1         0.1020    66.5      67.2   69.6
## 13    13    0.292  51.2         0.0976    65.5      66.3   68.9
## 14    14    0.292  47.5         0.0967    64.6      65.4   68.2
## 15    15    0.291  44.3         0.0955    63.7      64.6   67.5
## 16    16    0.290  41.5         0.0941    62.8      63.7   66.8
## 17    17    0.289  39.1         0.0927    61.9      62.9   66.1
## 18    18    0.288  36.9         0.0914    61.1      62.1   65.4
## 19    19    0.288  34.9         0.0900    60.2      61.2   64.7
## 20    20    0.287  33.2         0.0886    59.4      60.4   64.0
## 21    21    0.286  31.7         0.0883    58.6      59.6   63.4
## 22    22    0.285  30.2         0.0870    57.7      58.9   62.7
## 23    23    0.285  28.9         0.0855    56.9      58.1   62.1
## 24    24    0.284  27.7         0.0849    56.1      57.3   61.4
## 25    25    0.282  26.8         0.0835    55.4      56.6   60.8
## 26    26    0.281  25.8         0.0820    54.6      55.9   60.2
## 27    27    0.280  24.7         0.0802    53.9      55.1   59.6
## 28    28    0.279  23.9         0.0787    53.1      54.4   58.9
## 29    29    0.279  23.0         0.0776    52.4      53.7   58.3
## 30    30    0.278  22.3         0.0762    51.7      53.0   57.7

Gaussian Mixture Models with hard thresholding

Points don’t seem to follow a Gaussian distribution no matter the number of clusters, chose 4 groups following the best k from K-means because the methods are similar

n_clust = datExpr_redDim %>% Optimal_Clusters_GMM(max_clusters=50, criterion='BIC', plot_data=FALSE)
plot(n_clust, type='l', main='Bayesian Information Criterion to choose number of clusters')

best_k = 3 # copying k-means best_k
gmm = datExpr_redDim %>% GMM(best_k)
clusterings[['GMM']] = gmm$Log_likelihood %>% apply(1, which.max)

Plot of clusters with their centroids in gray

gmm_points = rbind(datExpr_redDim, setNames(data.frame(gmm$centroids), names(datExpr_redDim)))
gmm_labels = c(clusterings[['GMM']], rep(NA, best_k)) %>% as.factor
ggplotly(gmm_points %>% ggplot(aes(x=PC1, y=PC2, color=gmm_labels)) + geom_point() + theme_minimal())

rm(wss, datExpr_k_means, h_clusts, cc_output, best_k, ICA_output, ICA_clusters_names, 
   signals_w_kurtosis, n_clust, gmm, gmm_points, gmm_labels, network, dend_meta, 
   best_power, c, viridis_age_cols, create_viridis_dict, pca)